Question 8.5: Calculate the radius of the star Betelgeuse.

Since the star Betelgeuse has a temperature about one half the temperature of the Sun, each square meter of Betelgeuse emits about one sixteenth the amount of energy per second as a square meter of the Sun. The fact that Betelgeuse is one hundred thousand times more luminous than the Sun then implies that it has 1, 600, 000 times more surface area than the Sun. Since the surface area of a sphere is related to its radius by the formula, A = 4πR^{2}, the radius of a spherical object is proportional to the square root of its surface area. We may thus conclude that the radius of Betelgeuse is about equal to the square root of 1,600,000times the radius of the Sun. Using the fact that the radius of the Sun is 696, 000 km, we find that the radius of Betelgeuse is \sqrt{1,600,000}  × 696, 000 \ km = 880 million kilometers. In comparison, the distance of the Earth from the Sun is about 150 million kilometers, while the distance of Mars from the Sun is 228 million kilometers and the distance of Jupiter from the Sun is 778 million kilometers. If Betelgeuse were in the center of our solar system, its radius would reach out beyond the orbit of Jupiter.